Trigonometry Examples

$4.75 = 0.07 d^{\frac{3}{2}}$

Step 1

Rewrite the equation as $0.07 d^{\frac{3}{2}} = 4.75$ .

$0.07 d^{\frac{3}{2}} = 4.75$

Step 2

Divide each term in $0.07 d^{\frac{3}{2}} = 4.75$ by $0.07$ and simplify.

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Step 2.1

Divide each term in $0.07 d^{\frac{3}{2}} = 4.75$ by $0.07$ .

$\frac{0.07 d^{\frac{3}{2}}}{0.07} = \frac{4.75}{0.07}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor.

$\frac{0.07 d^{\frac{3}{2}}}{0.07} = \frac{4.75}{0.07}$

Step 2.2.2

Divide $d^{\frac{3}{2}}$ by $1$ .

$d^{\frac{3}{2}} = \frac{4.75}{0.07}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $4.75$ by $0.07$ .

$d^{\frac{3}{2}} = 67.\overline{857142}$

Step 3

Raise each side of the equation to the power of $\frac{2}{3}$ to eliminate the fractional exponent on the left side.

${(d^{\frac{3}{2}})}^{\frac{2}{3}} = {67.\overline{857142}}^{\frac{2}{3}}$

Step 4

Simplify the exponent.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify ${(d^{\frac{3}{2}})}^{\frac{2}{3}}$ .

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Step 4.1.1.1

Multiply the exponents in ${(d^{\frac{3}{2}})}^{\frac{2}{3}}$ .

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Step 4.1.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$d^{\frac{3}{2} \cdot \frac{2}{3}} = {67.\overline{857142}}^{\frac{2}{3}}$

Step 4.1.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.1.2.1

Cancel the common factor.

$d^{\frac{3}{2} \cdot \frac{2}{3}} = {67.\overline{857142}}^{\frac{2}{3}}$

Step 4.1.1.1.2.2

Rewrite the expression.

$d^{\frac{1}{2} \cdot 2} = {67.\overline{857142}}^{\frac{2}{3}}$

Step 4.1.1.1.3

Cancel the common factor of $2$ .

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Step 4.1.1.1.3.1

Cancel the common factor.

$d^{\frac{1}{2} \cdot 2} = {67.\overline{857142}}^{\frac{2}{3}}$

Step 4.1.1.1.3.2

Rewrite the expression.

$d^{1} = {67.\overline{857142}}^{\frac{2}{3}}$

Step 4.1.1.2

Simplify.

$d = {67.\overline{857142}}^{\frac{2}{3}}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Raise $67.\overline{857142}$ to the power of $\frac{2}{3}$ .

$d = 16.63656698$